#include "stdafx.h"

/*
 * -- SuperLU MT routine (version 2.0) --
 * Lawrence Berkeley National Lab, Univ. of California Berkeley,
 * and Xerox Palo Alto Research Center.
 * September 10, 2007
 *
 * History:     Modified from LAPACK routine ZGEEQU
 */
#include <math.h>
#include "hnum_pzsp_defs.h"

namespace harlinn
{
    namespace numerics
    {
        namespace SuperLU
        {
            namespace DoubleComplex
            {

                void
                zgsequ(SuperMatrix *A, double *r, double *c, double *rowcnd,
                        double *colcnd, double *amax, int *info)
                {
                /*    
                    Purpose   
                    =======   

                    zgsequ() computes row and column scalings intended to equilibrate an   
                    M-by-N sparse matrix A and reduce its condition number. R returns the row
                    scale factors and C the column scale factors, chosen to try to make   
                    the largest element in each row and column of the matrix B with   
                    elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.   

                    R(i) and C(j) are restricted to be between SMLNUM = smallest safe   
                    number and BIGNUM = largest safe number.  Use of these scaling   
                    factors is not guaranteed to reduce the condition number of A but   
                    works well in practice.   

                    See supermatrix.h for the definition of 'SuperMatrix' structure.
 
                    Arguments   
                    =========   

                    A       (input) SuperMatrix*
                            The matrix of dimension (A->nrow, A->ncol) whose equilibration
                            factors are to be computed. The type of A can be:
                            Stype = SLU_NC; Dtype = SLU_Z; Mtype = SLU_GE.
	    
                    R       (output) double*, size A->nrow
                            If INFO = 0 or INFO > M, R contains the row scale factors   
                            for A.
	    
                    C       (output) double*, size A->ncol
                            If INFO = 0,  C contains the column scale factors for A.
	    
                    ROWCND  (output) double*
                            If INFO = 0 or INFO > M, ROWCND contains the ratio of the   
                            smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and   
                            AMAX is neither too large nor too small, it is not worth   
                            scaling by R.
	    
                    COLCND  (output) double*
                            If INFO = 0, COLCND contains the ratio of the smallest   
                            C(i) to the largest C(i).  If COLCND >= 0.1, it is not   
                            worth scaling by C.
	    
                    AMAX    (output) double*
                            Absolute value of largest matrix element.  If AMAX is very   
                            close to overflow or very close to underflow, the matrix   
                            should be scaled.
	    
                    INFO    (output) int*
                            = 0:  successful exit   
                            < 0:  if INFO = -i, the i-th argument had an illegal value   
                            > 0:  if INFO = i,  and i is   
                                  <= M:  the i-th row of A is exactly zero   
                                  >  M:  the (i-M)-th column of A is exactly zero   

                    ===================================================================== 
                */

                    /* Local variables */
                    NCformat *Astore;
                    doublecomplex   *Aval;
                    int i, j, irow;
                    double rcmin, rcmax;
                    double bignum, smlnum;
                    
    
                    /* Test the input parameters. */
                    *info = 0;
                    if ( A->nrow < 0 || A->ncol < 0 ||
	                 A->Stype != SLU_NC || A->Dtype != SLU_Z || A->Mtype != SLU_GE )
	                *info = -1;
                    if (*info != 0) {
	                i = -(*info);
	                xerbla_("zgsequ", &i);
	                return;
                    }

                    /* Quick return if possible */
                    if ( A->nrow == 0 || A->ncol == 0 ) {
	                *rowcnd = 1.;
	                *colcnd = 1.;
	                *amax = 0.;
	                return;
                    }

                    Astore = (NCformat*)A->Store;
                    Aval = (doublecomplex*)Astore->nzval;
    
                    /* Get machine constants. */
                    smlnum = dlamch_("S");
                    bignum = 1. / smlnum;

                    /* Compute row scale factors. */
                    for (i = 0; i < A->nrow; ++i) r[i] = 0.;

                    /* Find the maximum element in each row. */
                    for (j = 0; j < A->ncol; ++j)
                        for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
                            irow = Astore->rowind[i];
                            r[irow] = SUPERLU_MAX( r[irow], z_abs1(&Aval[i]) );
	                }

                    /* Find the maximum and minimum scale factors. */
                    rcmin = bignum;
                    rcmax = 0.;
                    for (i = 0; i < A->nrow; ++i) {
	                rcmax = SUPERLU_MAX(rcmax, r[i]);
	                rcmin = SUPERLU_MIN(rcmin, r[i]);
                    }
                    *amax = rcmax;

                    if (rcmin == 0.) {
	                /* Find the first zero scale factor and return an error code. */
	                for (i = 0; i < A->nrow; ++i)
	                    if (r[i] == 0.) {
		                *info = i + 1;
		                return;
	                    }
                    } else {
	                /* Invert the scale factors. */
	                for (i = 0; i < A->nrow; ++i)
	                    r[i] = 1. / SUPERLU_MIN( SUPERLU_MAX( r[i], smlnum ), bignum );
	                /* Compute ROWCND = min(R(I)) / max(R(I)) */
	                *rowcnd = SUPERLU_MAX( rcmin, smlnum ) / SUPERLU_MIN( rcmax, bignum );
                    }

                    /* Compute column scale factors */
                    for (j = 0; j < A->ncol; ++j) c[j] = 0.;

                    /* Find the maximum element in each column, assuming the row
                       scalings computed above. */
                    for (j = 0; j < A->ncol; ++j)
	                for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) {
	                    irow = Astore->rowind[i];
                            c[j] = SUPERLU_MAX( c[j], z_abs1(&Aval[i]) * r[irow] );
	                }

                    /* Find the maximum and minimum scale factors. */
                    rcmin = bignum;
                    rcmax = 0.;
                    for (j = 0; j < A->ncol; ++j) {
	                rcmax = SUPERLU_MAX(rcmax, c[j]);
	                rcmin = SUPERLU_MIN(rcmin, c[j]);
                    }

                    if (rcmin == 0.) {
	                /* Find the first zero scale factor and return an error code. */
	                for (j = 0; j < A->ncol; ++j)
	                    if ( c[j] == 0. ) {
		                *info = A->nrow + j + 1;
		                return;
	                    }
                    } else {
	                /* Invert the scale factors. */
	                for (j = 0; j < A->ncol; ++j)
	                    c[j] = 1. / SUPERLU_MIN( SUPERLU_MAX( c[j], smlnum ), bignum);
	                /* Compute COLCND = min(C(J)) / max(C(J)) */
	                *colcnd = SUPERLU_MAX( rcmin, smlnum ) / SUPERLU_MIN( rcmax, bignum );
                    }

                    return;

                } /* zgsequ */

            };
        };
    };
};